Uncertainty quantification in passive microrheology*

Complex fluids have long been characterized by two functions that summarize the fluid’s elastic and viscous properties, the storage and loss moduli. Information about these bulk fluid properties can be inferred from the path statistics of immersed, fluctuating microparticles. In this talk, we describe a systematic study of this multi-step protocol and we analyze errors and uncertainties intrinsic to it. Particle velocities are assumed to be well-described by the Generalized Langevin Equation uniquely characterized by a memory kernel, which is hypothesized to be inherited from the surrounding fluid. We treat the reconstruction of the memory kernel as an inverse problem and apply nonlinear least-square optimization to numerically generated data to obtain parameters for different linear viscoelastic models. We show that, despite the fact that certain parameters are essentially unidentifiable on their own, the protocol is remarkably effective in reconstructing the storage and loss moduli in a range that corresponds to the experimentally observable regime. We also discuss the errors associated with different numerical approximation of the Laplace transform of the mean square displacement.